By M. R. SPIEGEL
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Additional info for Schaum's Handbook of Math Formulas and Tables
Example text
FORMULAS E FROM OQ E SOLID ANALYTIC C tA (L FW U L 51 GEOMETRY E A TTx I S N N HI ~P a Eb T D O, ,S M, E N y O dI Fig. 12-10 E 1 C 2 w I L W Y . a I a sh b = a i b A I xL A X I 2 , f A L o re ee ac c ST I X PI H N I S T D S I 6 fs e l t e c mr r e l io r c y u rf ie o c i a o l . c - s t p d mi u a i s i t en l x u sd Fig. 12-11 E 1 2 C . L W AO 2 L A I z A XN J ST X IE P H I S T S 7 Fig. 12-12 H 1 2 $ . Y O z+ 1 2 $ O S P F 8 _ N H E E $ Fig. 12-13 E R E B I 5 2 FORMULAS FROM SOLID H Note orientation of axes ANALYTIC YO in Fig.
10 . cn + c 7 HYPOCYCLOID 1 , e o i C O = 6e nc rn ei p a i e bu a p ei x l r a & Y - C r = 3f . n o a u (s + + r i d\ , , \ )! 5 t s) t’=3 4 n \ s G a 4e tA r z 2 v i ic f a i sd d e tv er c r nr F d 1 e d he d i e c l ti i e i 1 u l e b g - u s . 14 Arc length of curve r = a(1 + COS0) = $XL~ = 8a This is the curve described by a point P of a circle of radius a as it rolls on the outside of a fixed circle of radius a. 321. Fig. 15 Equation: Y z : (&/a + e-x/a) = a coshs This is the eurve in which a heavy uniform cham would hang if suspended vertically from fixed points A anda.
A &f . 11 A u b l T i a c a i r o /t brc o e r e u y 2 Z a = a s li dh s bu a p ei P o si t o o a n c4h n o rl f d A o ’ s \ l ’ eB, / xg n n i 1 1 g- l m i 2 , tY n- nn j m i O : e o t n n S a # h ) 2 c g h t v i ic f a g is h er nr n. F 1 d c ti g i 1 i l b g - u ViflTH FOUR CUSf’S / Z c 2 a f 9o o 3 Z r O 0 f= n6 c a 1 o ss o r n n 8 o Z l u a r a a t m 3 ar ta n gr ya r c o ss o r n v i ai e s f al r. i d m i : n o i g n e o t n 9 n a 40 t 3 r S nu t 3 i o = & yeu ec r e i F ) a a ya r c . 10 .